A discrete mathematics problem by Anthony Pham

An ant is on a regular tetrahedron, where all the edges are 1 meter long. The ant, starting on a vertex, randomly chooses and crawls to another vertex, and repeats. The probability that the ant is back to the same vertex after crawling 5 meters can be written as \(\frac{p}{q} \). If p and q are coprime, what is p+q?